Determine how many solutions exist for the system of equations. ${x-y = -9}$ ${-5x+y = -9}$
Solution: Convert both equations to slope-intercept form: ${x-y = -9}$ $x{-x} - y = -9{-x}$ $-y = -9-x$ $y = 9+x$ ${y = x+9}$ ${-5x+y = -9}$ $-5x{+5x} + y = -9{+5x}$ $y = -9+5x$ ${y = 5x-9}$ Just by looking at both equations in slope-intercept form, what can you determine? ${y = x+9}$ ${y = 5x-9}$ The linear equations have different slopes. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ When two equations have different slopes, the lines will intersect once with one solution.